Modeling temperature polarization phenomena for longitudinal shell-side flow in membrane distillation process

The analytical solution for longitudinal heat constituent to be used as the main submodel for the temperature polarization phenomenon (TP) has been developed. The presented solution is fragment of advanced model of multistage hybrid membrane-based process. The model developed for sophisticated configuration of shell-side spacing in tubular-type unit. Balance equations for viscous and temperature boundary layers are the core of the model. Integration of equations for temperature and hydrodynamic field over the control volume of shell-side spacing configuration has been carried out and analytical solution was obtained. The solution is applicable to laminar, incompressible and continuous now in shell-side spacing of tubular-type unit. The solution describes an uniform longitudinal flux along triangular membrane array. The solution does not contain differential terms and permits simulation and analysis of the influence of various factors as well. The calculated data are attached.